Some Studies Of The Normal Subsemigroup Of Inverse Semigroups

In this paper, we study some properties of the normal subsemigroup lattices of inverse semigroups and describe the relationship between the normal subsemigroup lattices (SubnS) of semigroups (S) and the normal subgroup lattices (Subng(S/σ))of maximal group homomorphism image (S/σ) of S. It is also shown that Brandt semigroup (S) whose normal subsemigroup lattices is distributive if and only if S is either a locally cyclic group with zero or Brandt semigroup B5. The necessary and sufficient conditions of Brandt semigroup (S) whose normal subsemigroup lattices is 0-distributive are shown.